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/* acoshf.c
*
* Inverse hyperbolic cosine
*
*
*
* SYNOPSIS:
*
* float x, y, acoshf();
*
* y = acoshf( x );
*
*
*
* DESCRIPTION:
*
* Returns inverse hyperbolic cosine of argument.
*
* If 1 <= x < 1.5, a polynomial approximation
*
* sqrt(z) * P(z)
*
* where z = x-1, is used. Otherwise,
*
* acosh(x) = log( x + sqrt( (x-1)(x+1) ).
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE 1,3 100000 1.8e-7 3.9e-8
* IEEE 1,2000 100000 3.0e-8
*
*
* ERROR MESSAGES:
*
* message condition value returned
* acoshf domain |x| < 1 0.0
*
*/
/* acosh.c */
/*
Cephes Math Library Release 2.2: June, 1992
Copyright 1984, 1987, 1988, 1992 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/
/* Single precision inverse hyperbolic cosine
* test interval: [1.0, 1.5]
* trials: 10000
* peak relative error: 1.7e-7
* rms relative error: 5.0e-8
*
* Copyright (C) 1989 by Stephen L. Moshier. All rights reserved.
*/
#include <math.h>
extern float LOGE2F;
float sqrtf( float );
float logf( float );
float acoshf( float xx )
{
float x, z;
x = xx;
if( x < 1.0 )
{
mtherr( "acoshf", DOMAIN );
return(0.0);
}
if( x > 1500.0 )
return( logf(x) + LOGE2F );
z = x - 1.0;
if( z < 0.5 )
{
z =
(((( 1.7596881071E-3 * z
- 7.5272886713E-3) * z
+ 2.6454905019E-2) * z
- 1.1784741703E-1) * z
+ 1.4142135263E0) * sqrtf( z );
}
else
{
z = sqrtf( z*(x+1.0) );
z = logf(x + z);
}
return( z );
}
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